The present invention relates to a branch circuit monitor and, more particularly, to a method of compensating for phase error when making a power measurement with a branch circuit monitor.
The total power consumption of a building or other facility is monitored by the electric utility with a power meter located between the utility's distribution transformer and the facility's power distribution panel. However, in many instances it is desirable to sub-meter or attribute the facility's power usage and cost to different occupancies, buildings, departments, or cost centers within the facility or to monitor the power consumption of individual loads or groups of loads, such as motors, lighting, heating units, cooling units, machinery, etc. These single phase or multi-phase electrical loads are typically connected to one or more of the branch circuits that extend from the facility's power distribution panel. While a power meter may be installed at any location between a load and the distribution panel, it is often advantageous to install a power meter capable of monitoring a plurality of circuits proximate the power distribution panel to provide centralized monitoring of the various loads powered from the panel.
Flexibility has favored adoption of digital branch circuit monitors incorporating data processing systems that can monitor a plurality of circuits and determine a number of parameters related to electricity consumption. A branch circuit monitor for measuring electricity consumption by respective branch circuits comprises a plurality of voltage and current transducers that are periodically read by the monitor's data processing unit which, in a typical branch circuit monitor, comprises one or more microprocessors or digital signal processors (DSP). The data processing unit periodically reads and stores the outputs of the transducers quantifying the magnitudes of current and voltage samples and, using that data, calculates the current, voltage, power, and other electrical parameters, such as active power, apparent power and reactive power that quantify the distribution and consumption of electricity. The calculated parameters are typically output to a display for immediate viewing or transmitted from the meter's communications interface to another data processing system, such as a building management computer for remote display or further processing, for example formulating instructions to automated building equipment.
The voltage transducers of digital branch circuit monitors commonly comprise a voltage divider network that is connected to a conductor in which the voltage will be measured. The power distribution panel provides a convenient location for connecting the voltage transducers because typically each phase of the electricity is delivered to the power distribution panel on a separate bus bar and the voltage and phase is the same for all loads attached to the respective bus bar. Interconnection of a voltage transducer and the facility's wiring is facilitated by wiring connections in the power distribution panel, however, the voltage transducer(s) can be interconnected anywhere in the wiring that connects the supply and a load, including at the load's terminals.
The current transducers of digital power meters typically comprise current transformers that encircle each of the power cables that connect each branch circuit to the bus bar(s) of the distribution panel. Bowman et al., U.S. Pat. No. 6,937,003 B2, discloses a branch circuit monitoring system that includes a plurality of current transformers mounted on a common support facilitating installation of a branch circuit monitor in an electrical distribution panel. For example, a branch circuit monitor produced by Veris Industries, LLC. commonly includes 84 current sensors; 21 current transformers mounted on each of four supports.
A current transformer typically comprises multiple turns of wire wrapped around the cross-section of a toroidal core. The power cable conducting the load current is passed through the aperture in the center of the toroidal core and constitutes the primary winding of the transformer and the wire wrapped around the cross-section of the core comprises the secondary winding of the transformer. Current flowing in the primary winding (primary current) induces a secondary voltage and current in the secondary winding which is quantitatively related to the current in the primary winding. The secondary winding is typically connected to a resistor network and the magnitude of the primary current can be determined from the amplitude of the voltage at the output of the resistor network. Since the primary winding comprises a single turn, the secondary current is, ideally, precisely equal to the load current in the primary winding divided by the number of turns in the secondary winding, that is:I1=I2(n)  (1)
where n=number of turns in the secondary winding.
However, actual transformers are not ideal transformers and the magnetization of the core of the current transformer produces errors that reduce the accuracy of the readings produced by the meter. Part of the current in the primary winding is used to magnetize the transformer core with the result that the secondary current is less than the product of the primary current and the ratio of turns in the primary and secondary windings (turns ratio). Referring to FIG. 1, the ratio error (re) varies with the magnitude of the primary current (I1) as follows:re(%)=K3+K4(log I1)  (2)
where K3 and K4 are constants.
The effect of the ratio error is to alter the relationship between the magnitudes of the measured secondary current (I2) and the primary current (I1) from the theoretical relationship to the relationship:
                              I          1                =                              I            2            ′                    ⁡                      (                          n              +                                                nr                  e                                100                                      )                                              (        3        )            
where I′2=measured secondary current
The magnitude of the measured secondary current (I2′) is related to the theoretical secondary current (I2), as follows:
                              I          2                =                              I            2            ′                    ⁡                      (                          1              +                                                r                  e                                100                                      )                                              (        4        )            In addition, the magnetization of the transformer core and windings causes a phase shift between the current in the primary winding and the current in the secondary winding. Since the transformer core is inductive in nature, the phase shift causes the phase of the secondary current to lag the phase of the primary current. Referring to FIG. 2, the resulting phase error (pe) varies with the magnitude of the primary current (I1) approximately according to the relationship:pe=K1+K2(I1−M)  (5)
where M, K1 and K2 are constants
In practice M is often approximately equal to ½ and, consequently, a square root approximation can often be conveniently employed as part of the overall correction algorithm. The values of the constants K1, K2, K3, and K4 depend upon the configuration of the particular current transformer. Factors such as core material and turns ratio affect the values of the constants which are typically ascertained by experiment with samples of a given core configuration. Typically, the values of K1, K2, K3, and K4 are determined for a particular transformer configuration or production batch by comparing the actual performance of a sample of the transformer configuration to the performance of a standard device when the secondary winding is connected in parallel to a particular impedance or burden.
In the typical digital power meter, instantaneous values of the sinusoidal analog voltage and current waveforms are digitally captured by periodically, simultaneously sampling the amplitudes of the outputs of respective voltage and current transducers. The effective power is approximated by averaging the sum of the products of the temporally corresponding instantaneous samples of the load voltage and current for each of the plurality of sampling intervals making up at least one cycle of the sinusoidal waveform:
                    P        ≅                              1            T                    ⁢                                    ∑                              k                =                1                                            k                =                                  T                                      Δ                    ⁢                                                                                  ⁢                    t                                                                        ⁢                                                  ⁢                                          v                ⁡                                  (                  k                  )                                            ⁢                              i                ⁡                                  (                  k                  )                                            ⁢              Δ              ⁢                                                          ⁢              t                                                          (        6        )                            where: P=effective power                    v(k)=sample voltage for the k-th sample, for example voltage 24            i(k)=sample current for the k-th sample, for example current 26            Δt=sampling interval                        
Before calculating electrical parameters based on the current, such as real power, total power, reactive power etc., the data processing system typically adjusts the value of the instantaneous load current to compensate for the effects of phase error and ratio error introduced by the current transformer. Typically, an initial or assumed value of the primary or load current is determined from the theoretical relationship of the primary current and the secondary current for an ideal transformer, equation (1), and the instantaneous measured secondary current. Then using the assumed load current, the data processing system accesses one or more ratio and phase error correction factors that are typically stored in a table or an equation in a memory and, using a correction algorithm, applies the correction factors to the assumed load current to calculate the adjusted or actual load current. To obtain accurate results, the phase and ratio error correction factors must be available for all possible values of the instantaneous current in the meter's operating range and the correction factors are commonly stored in the form of a table, a mathematical formula, or another form representing error correction as a function of the instantaneous primary current. Substantial data storage capacity is necessary to store the required data for correcting currents throughout the meter's operating range and substantial processing power is required to apply the appropriate correction factors to each of the instantaneous load currents calculated from the samples of the secondary current.
Bruno, U.S. Pat. No. 7,359,809, incorporated herein by reference, discloses a meter and a method of determining current in which the root mean square (rms) current of a plurality of accumulated current samples is calculated and used to determine the phase error correction for the current sensor. The phase error and the ratio error correction factors are then applied to one or more current samples to determine the corrected magnitudes of the instantaneous current samples. Since the rms current varies much slower than the instantaneous current, the data processing resources of the meter can be significantly reduced.
Bruno, U.S. Pat. No. 7,447,603, incorporated herein by reference, discloses a power meter in which the phase error is determined from the rms current or otherwise and the reading of respective voltage and current sensors are temporally offset by a time differential equivalent to the phase error so that the phase error is accounted for in the instantaneous values of voltage samples that correspond to respective current samples. While temporally offsetting the current and voltage sampling to accommodate phase error significantly reduces the data processing requirements of the meter, the differential between the current sampling and the voltage sampling can make it difficult to sample at a sufficiently high frequency to accommodate the large number of current sensors that characterize a branch circuit monitor and can interfere with obtaining a sufficient number of current samples from each of the sensors during each AC cycle to adequately describe the current waveform to avoid aliasing. In addition, due to the large number of current sensors that characterize a branch circuit monitor, capturing a voltage sample corresponding to each of the current samples produces a substantial number of voltage samples increasing the bandwidth and the cost of the data processing unit of the meter.
What is desired, therefore, is a branch circuit monitor and a method of operating a branch circuit monitor enabling current sampling at a high frequency but requiring a relatively low bandwidth while providing phase error corrected electrical measurements for a substantial number of monitored circuits.